6) The profit function for sales of two models of trucks at a car dealership is given by (a, b) = 1240a + 800b – 5a² + 2ab – 6b² – 250 where a is the number of sales per week of model A, and b is the number of sales per week of model B. What's the marginal profit if model A sales increase by 1 unit from a base of II(15,10)? You must use calculus to solve. Interpret the result.
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- Given that the relationship between the sales price for one of a company’s products and the quantity sold per month is D = 500 – 5p units where D is the demand or quantity sold per month and p is the unit price in dollars. The fixed cost is $1,000 per month, and the variable cost is $20 per unit produced. (a) Determine the optimal number of units that should be produced and sold per month. (b) What is the maximum profit per month related to the product? (c) What is the company’s range of profitable demand? Support your answers graphically.Ken’s firm is committed to reducing greenhouse gas by 10 tons per year. The firm’s cost of abating a ton of carbon is shown below: Quantity of Carbon Abated in tons Marginal Cost of Carbon Abatement 1 $3 2 $4 3 $5 4 $6 5 $7 6 $8 7 $9 8 $10 9 $11 10 $12 Ken also has the option to instead pay for a reforestation project that offsets a ton of carbon. Each reforestation project cost $7. What is the best combination of production abatement and reforestation abatement for Ken? How much money does Ken save byusing the reforestation abatement?A company has determined that the price and the monthly demand of one of its products are related by the equation D = √(400 − p), where p is the price per unit in dollars and D is the monthly demand. The associated fixed costs are $1,125/month, and the variable costs are $100/unit. Use this information to answer What is the optimal number of units that should be produced and sold each month? (a) 10 units (b) 15 units (c) 20 units (d) 25 units. Select the closest answer.
- PUP 48,213 UST 40,000 FEU 27,889 LRT2 200,000 passengers daily If 60% of PUP, 30% of UST, and 85% of FEU students take LRT2 daily and pays an average fare of Php25 per day… What is the total annual market size (revenue) of LRT2? What is the total annual market size (revenue) of the 3 schools? If operations is halted for 1 week, what is the projected loss in revenues? What is the market share (volume) of: PUP students? UST students? Feu students?A company has established that the relationship between the sales price for one of its products and the quantity sold per month is approximately p = 78 – 0.11D units. The fixed cost is $800 per month and the variable cost $32 per unit produced. What number of units, D*,should be produced per month and sold to maximize the profit per month related to the product? Round your answer to 2 decimal places.A company has determined that the price and the monthly demand of one of its products are related by the equation D = (400 - P)1/2 , where p is the price per unit in dollars and D is the monthly demand. If the associated fixed costs are $1,125/month, and the variable costs are $100/unit, what is the optimal number of units that should be produced and sold each month to maximize the profit?
- Problem 2: Assume that a company has the following data for one of its manufacturing cells:Theoretical velocity: 40 units per hourProductive minutes available (per year): 1,200,000Annual conversion costs: $4,800,000Actual velocity: 30 units per hourRequired:1. Calculate the actual conversion cost per unit using actual cycle time and the standardcost per minute.2. Calculate the ideal conversion cost per unit using theoretical cycle time and the standardcost per minute. What incentive exists for managers when cycle time costing is used?3. What if the actual velocity is 36 units per hour? What is the conversion cost perunit? What effect will this improvement have on delivery performance? Cheat Notes :Cycle time (time/units produced)velocity (units produced/time)1. XYZ company’s marketing department recommends to manufacture and market a newe co-friendly and sustainable product. The financial department provides the following cost Php 6,000 is the estimated fixed costs and the estimated variable cost is Php 100 per unit. The revenue function is given with an equation of 150x - 0.005x2. Determine the following: a) the optimal demand and value (Php) b)The demand in unit and amount (Php) that will give highest revenue c) Break even points and range of profitabilityA companies has invested $ 1 million in the purchase of new machinery in its plant and does not intend to incur major capital expenditure over the next two years. The companies can manufacture a product according to the annual production function: \ (Q (L) = 30L-L ^ 2 \) , while the annual labor costs (in $ 000's) of are given by the function \ (C (L (L ) = 4L ^ 2 + 20L \) . The companies sells the product at $ 10,000 per unit. a) Determine the optimal level of production and labor in order to maximize profits. b) Find annual profits. c) Calculate the present value of the net profit achieved during 2 years of production assuming an interest rate of 5%.
- A local defense contractor is considering the production of fireworks as a way to reduce dependence on the military. The variable cost per unit is $40D. The fixed cost that can be allocated to the production of fireworks is negligible. The price changed per unit will be determined by the equation p=$180-(5)D, where D represents demand in units sold per week. a.What is the optimum number of units the defense contractor should produce in order to maximize profit per week? b.What is the profit if the optimum number of units are produced?A local defense contractor is considering the production of fireworks as a way to reduce dependence on the military. The variable cost per unit is $40D. The fixed cost that can be allocated to the production of fireworks is negligible. The price changed per unit will be determined by the equation p=$180-(5)D, where D represents demand in units sold per week. a.What is the optimum number of units the defense contractor should produce in order to maximize profit per week? b.What is the profit if the optimum number of units are produced? Show handwritten solutionsThe cost of producing 5-gallon water bottles is given by C(q) = 0.005q2 + 2q + 1000. If 2000 5-gallon water bottles are produced, fint the average cost